Basically it seems as though the eyes are only targeting the "original three" strongholds in first ring. Created world (seed: 5428015623262890092), teleported out to 27000,~,4000 (which seems like it would be just outside the outer most ring of strongholds) and attempted to located one in this ring with the eyes.

They only ever targeted "roughly" the origin of the map, I suspect because they were targeting one of the 3 in the first ring near the origin.

After several uses, i resorted to using the eye, then teleporting ~1000 blocks toward the origin and re-used each time. I never once saw the eye switch directions and point at anything other than back toward the origin. I would expect that it would point away from the origin at some point within that outer most ring. But instead I repeated this process until I was led back to roughly the origin, and then was able to locate a stronghold at -692,34,577. Interestingly enough, UNDER A MOOSHROOM ISLAND! (I thought that was cool).

[OP has removed this whole bit about the JIRA search function. It, and it alone, was a joke.]